Finally, as an example that does not meet the conditions of a social dilemma, we consider the battle of the sexes [1]}. Here, the payoff ranking is \(S>T>R\geqslant P\) . The one-shot version of this game has two pure equilibria, but players disagree on which equilibrium they prefer. When two selfish learners engage in the repeated game, they frequently converge toward one of these pure one-shot equilibria (Fig. REF d). In contrast, groups with at least one FMTL player again reliably learn to alternate (Fig. REF e,f). Selfish learning is already able to generate efficient outcomes, but only FMTL can guarantee that the realized outcome is fair, irrespective of the learning rule of the opponent.
